Preliminary remark Subspace as shown in Star Trek does not
exist in present-day physics as a reality or only a theory. It is a concept of
storytelling. Subspace is necessary because FTL travel is impossible within the boundaries of
special relativity as outlined in Chapter 1.2. Being part of a fictional
universe, subspace has not been developed
by far as consequently as
a truly scientific idea would have required. On the contrary, everything we know
about subspace is based on more or less random and often contradictory canon
evidence.

Important note
A Google search for
"subspace" gives us more than 90% Trek-related results. Most of the rest refers
to concepts where a subspace is a subset to a space in a
mathematical sense. In other words, the real subspace is a
generic mathematical model, whereas Trek's subspace denotes a
specific physical concept. The equal naming is nothing more than a coincidence.

Much of the following is speculation and not
strictly based on observations, but it is conceived to comply with them. Some
prominent subspace characteristics and phenomena will be made more plausible. Still, some contradictory
evidence may remain simply because subspace was never meant to represent a scientific
theory.

Definition There is no
canon definition of what subspace actually is. But there are countless canon accounts
on subspace that allow to make a couple of presuppositions.

1. Subspace must be present everywhere in the
universe because sensors can measure subspace distortions wherever deemed
necessary. So it looks like for every point in our space there is a
corresponding point in subspace, otherwise the various measurements of subspace
stress in a certain region of space and of the warp field which obviously has a
spatially limited effect on subspace would make no sense.

2. It appears that subspace
is a
continuum in addition to and outside of the three dimensions of our normal space and to time.
Subspace may be described as a dimension, and there would be plenty of them left
in present-day string theories that subspace could represent. But it is most likely not
equivalent to a fourth spatial dimension, since it exhibits
considerably different characteristics than the three familiar dimensions.
Submerging into subspace is not like moving in normal space. This
specialty of subspace is not unlike the dimension of time. Time is not
equivalent to spatial coordinates either, since "time's
arrow" dictates a preferred direction. Consequently, we would not expect
subspace "distances" to be measured in meters (or even in seconds).

3. Transitions of matter or energy
into subspace or, vice
versa, from subspace into real space might occur naturally. Subspace itself or
domains accessible only through subspace are even believed to be populated by
indigenous lifeforms (see 3.5 Subspace Phenomena). It really
exists as a physical domain and not just as a mathematical model illustrating
the effects of FTL propulsion.

4. Still, the presence of subspace as depicted in Star Trek is beyond human perception
as long as we are confined to our space-time, and it can only be verified with special measuring
equipment of the future. The frequent light
effects connected with subspace may be explained away in that they are secondary
effects in our space, which are typical of, but not a definite indicator of the
presence of a subspace phenomenon. In other words, present-day equipment
wouldn't detect anything outlandish about subspace light effects, because it's
just light. Only that we may not be able to explain where it comes from and why without the
knowledge of subspace.

Subspace vs. hyperspace "Hyperspace" is another term frequently used in
science fiction. It seems that most science fiction is using a concept of folded
space for FTL travel, bringing two points in space closer together in a higher
dimension -- hyperspace. This is much the same as the concept of wormholes which
are commonplace in Star Trek too. It is quite obvious that subspace in Star Trek
is supposed to be something different - not only quantitatively (Star Trek ships
with warp drive are considerably slower than if they were passing through a
wormhole), but also qualitatively (ships at warp always remain practically in
our space-time, whereas wormhole/hyperspace travelers definitely don't).
Hyperspace was only mentioned very few times in Star Trek, and mostly by accident
like a few times on TNG. We wouldn't expect the two domains to be identical, and
they have different (even opposite) names. So where "hyperspace" was used
like "subspace" on screen, we should either imagine that the
characters actually said
"subspace" (the convenient solution) or assume that they were really
talking about something different, much less common than subspace.

3.2 Subspace
Models

Premise We assume that subspace is a physical reality, an
inhabitable realm and not just a mathematical model. Yet, in both cases we would
have to describe how subspace could look like from the inside and how it could relate
to real space. This chapter attempts to create a theoretical
foundation for everything that we know about the structure of subspace from canon accounts.

Continuous vs. discrete model
Fig. 3.1 depicts a three-dimensional
representation of the four-dimensional combination of space (x,y,z) and subspace
(zeta). The model on the left is continuous, the one on the right exhibits
distinct layers of subspace. In both models our three-dimensional space is just
a part of a whole which we may call subspace. Only the two dimensions x and y of normal space are shown. The third
axis with the coordinate zeta is what we can call the "subspace depth"
which, as mentioned above, probably isn't measured in meters or other length
units because subspace is not akin to a spatial dimension. In TNG:
"Schisms" Geordi identified Riker's homing signal as coming from an
energy level of 16.2 keV, which indicates that the scale of "subspace
depth" may be an energy scale.

Fig. 3.1 Continuous (left) and discrete (right) subspace model

In the
continuous model (Fig. 3.1 left) our normal space is comprised just of the very surface (x,y,zeta=0)
of a subspace continuum. Zeta is continuous just like x and y too and may assume
any
positive real value, while zeta<0 remains undefined. Any point in the x-y plane has
an infinite number of corresponding points in subspace along the zeta-axis. This is the
model we are likely to apply as a first approach, assuming that x,y,z as well as
time are continuous (at least to our perception and within the accuracy of conventional measuring
equipment), and that there would be no reason why the same should not
apply to subspace. But this model may turn out flawed.

The discrete model (Fig. 3.1 right) may work
better to describe the expected as well as the observed properties of subspace.
In this model, there is no continuous "subspace depth" zeta any
longer. Instead of that, subspace is divided into discrete layers which I have given tentative numbers
k starting with "0". Within each layer, the
properties of subspace are changing only slightly or are even constant, while
there is some sort of barrier between each two layers. We may imagine that considerably
more energy has to be expended to move from one layer to the next one than
inside the same layer. The bright green uppermost layer numbered with "0" is identical to
normal space.

Side note
The concept of energy barriers
is quite common in solid-state physics and particularly important to describe semiconductors. Any
solitary atom exhibits discrete energy
levels. In an extended solid-state material, these energy levels join to bands which are continuous in
x,y,z and allow spatial charge transport if
the band is not already fully occupied. There are band gaps which are not
allowed to be occupied by charge carriers. In order to make the transition
from one band to a higher (and emptier) one, it is necessary to supply a
sufficient energy in the form of light, voltage or heat, corresponding to the
width of the band gap.

The first problem with the continuous
approach is that normal space would have to occupy a "thickness" of
exactly zero. But realistically, there would have to be natural fluctuations
("zero-point energy"). Anyone or anything in our world would not always be exactly
in real space, but slightly submerged into subspace. Perhaps this natural
fluctuation is small enough to evade our senses, and it may have influenced any
physical experiments prior to the discovery of subspace only below the
measurement limit, so it remained unnoticed. Still, there is the problem that
the subspace axis extends only in one direction, that there are supposed to be
no negative values. As a result, the average of all fluctuations of normal space
could not be found at zeta=0, but at a small subspace depth zeta>0. In other
words, the actual normal space as found by measurements would not be equal to
the theoretical normal space at the very surface of the continuum. It may be
suggested that negative subspace is actually identical to hyperspace, but we
would expect hyperspace to have completely different properties which may not be
explained with a simple sign reversal. Summarizing, using a discrete model, it is much easier
to explain why subspace is not within the limits of our perception and measuring
equipment, the reason being that first a threshold has to be crossed to become
aware of the existence of subspace. Some sort of exotic energy is required in
considerable amounts to that end, energy which naturally exists because of
quantum fluctuations only in minute amounts.

The second flaw of the continuous approach is
more straightforward. We know that there are peak transitional thresholds between the
familiar warp factors at which the energy expenditure rises strongly. More
precisely, these thresholds even define the warp factors, as a look at the
official diagram from the TNG Technical Manual[Ste91]
reveals (part of it was clearly visible on screen in ENT: "First
Flight" too). It seems logical that
this observation is attributed to the structure of subspace. In other words, the
peak transitional thresholds most likely exist due to transitions from one
subspace layer to another. Alternatively, the peak transitional thresholds might
reflect just the technical principle of the ship's engines, but in this case the the
scale would be far less universal. It would change too often following progress
in propulsion technology, and the warp factors would depend on the ship class,
maybe even on how the drive is tuned on an individual ship.

In addition, we have evidence from TNG:
"Schisms" that the aliens' inhabitable domain is located in a "tertiary
subspace manifold", which sounds very much like subspace consists of
discrete layers. Geordi also mentions "subspace bands" in the
episode, but just like radio frequency bands these may be defined more or less
arbitrarily even in a continuous subspace model.

Inside subspace
Having decided that subspace most likely has a discrete structure, it needs to
be clarified what is the difference between the single subspace layers. The
first assumption is that subspace layer 1 should be "somewhere else"
than the normal space layer 0, as seen most obviously in TNG:
"Schisms" where crew members were abducted into subspace by aliens.
The realm shown in the episode looked much like our normal space, but was
obviously not present in normal space at any place x,y,z or any time t (it was
explicitly mentioned in the episode to be a "tertiary subspace
manifold/domain"). Although
we cannot be sure whether the alien realms in "Schisms" as well as in
VOY: "Heroes and Demons" or VOY: "Bride of Chaotica" are not
actually already in a parallel space/universe (see Fig. 3.4), there should be some
inhabitable place "inside subspace" too if there is something like that on either side of it. In other
words, if subspace is always talked about like an extended domain, why should it
be only some sort of uninhabitable gate between the universes in reality?

There must be some sort of difference between
the single layers. Regardless of the nature of this difference, we may imagine that subspace differs the more from normal
space the further
"below" the layer is located. We may say that subspace should become
the more "exotic" the deeper we submerge into it. It is just
speculation, but we may think of a model in which the subspace layers form some
sort of funnel. In Fig. 3.1 we could see that each point in normal space-time
(with just the x-y plane depicted) corresponds with one point at a given
"depth" zeta (continuous) or k (discrete), still assuming that
subspace has the same "lateral" geometry (in x-y) as normal space. Fig. 3.3
illustrates how a region in normal space could be related to gradually denser
subspace layers. This compression could be the key to warp propulsion, transwarp
and FTL communication, considering that the distances to be bridged in subspace
in a given time shrink with respect to normal space! This way subspace can be a
shortcut through space.

Fig. 3.3 Model of gradually compressed subspace

Unlike it is the case with wormholes or with
some of the natural or artificial
anomalies discussed below, these funnels are just illustrations of how
subspace relates to normal space. They are no dedicated gates. Subspace is
usually "flat" in a similar fashion as normal space-time is homogenous,
at least in the absence of a mass that could distort it, according to general relativity. In a "flat" subspace one could draw such a funnel for
each possible square unit in the x-y plane. Also, no starship entering subspace would
"fall" into such a funnel. On the contrary, seeing how the layers are
likely separated by energy barriers or peak transitional thresholds, they could
much easier move within one plane than between the planes.

The far end
We may go one step further and ponder where the bottom of subspace is located,
and if the funnels ends up in a singularity, a depth in which all the reference
points to our universe merge to one single point. In such a singularity space
would be concentrated much like mass is concentrated in a single point in a
mathematical model of a black hole. This is the point that Tom Paris would have
arrived at in VOY: "Threshold" if we believe the fairy-tale of
"infinite speed". But what if subspace actually doesn't reach down to
such a singularity, if after passing a number of compressed layers its
density drops again? This would be equivalent to approaching normal space again,
yet on the "other side" of subspace. Passing through all subspace
layers may take us to a parallel universe! This idea is illustrated in Fig. 3.4.
It is undetermined how many parallel universes exist and which funnel leads to
which universe. It may depend on when and how the parallel universe came to
life. But basically it would be possible to have just one parallel universe like
the one of TOS: "Mirror, Mirror", as well as an immense number like in
TNG: "Parallels".

Evidence for the existence of parallel
universes accessible through subspace can be found in DS9: "Playing
God" where the protouniverse started off as a subspace phenomenon. The
strange realms within subspace where fantasy becomes reality, like in TNG: "Where No One Has Gone
Before" and "Remember Me", and perhaps also the aliens' inhabitable
domain in "Schisms" may be well
regarded as either deep in subspace or already beyond the far end of subspace.

Now we have to do just one more thing. We
need to translate the "geocentric" model in Fig. 3.4 which arrogantly
puts our universe above everything else to an absolute model in which our
universe is just one among many others. This is shown in Fig. 3.5 where the
irregularity is intentional to demonstrate that universes embedded into a
subspace substrate may be regarded like galaxies inside the dimensions of space.

Premise Subspace is the domain which enables warp propulsion, at least in the type of
warp drive used on Federation starships and those of most known races in Star
Trek. We know from many statements in episodes that the warp engine generates a
warp field that totally encompasses the starship. The warp field corresponds to
a distortion of
subspace. The subspace field stress is the defining quantity of a subspace or
warp field and is measured in cochranes. At a field stress
of more than 1 cochrane we obtain a warp field which, with the right frequency
and geometry tuning, may become a propulsive asymmetric warp field, as outlined
in the TNG Technical Manual[Ste91]. The TNGTM
describes such a warp field as a combination of different nested layers, "each
layer exerting a controlled amount of force against its next-outermost
neighbor." This coupling of nested layers which correspond to different
frames of reference can be supposed to enable FTL speeds because between each
two layers the effective relative speed would remain below c. Still, with no
more than 9 layers the attainable speed could be no more than 9c.
Star Trek's warp drive circumvents the limitations of special
relativity, but there must be something special about subspace as a frame of
reference in addition. As outlined in the previous
chapter, one idea is that the structure of subspace may be such that corresponding points
in space are closer together in subspace.

Side note A more elaborate and in several ways
different treatise on the nature of subspace fields is Subspace
Physics[Hin2] at Jason Hinson's site

In order to achieve superluminal speeds, would the ship
itself have to submerge into subspace and hence into a separate domain, like it
is with (hyperspace) jump gates or with wormholes? Not necessarily. The term
"subspace field" itself, as well as the fact that the ship is not
visibly in a different realm during normal warp travel indicate that it may
still be in normal space. Conversely, with the various transwarp drives or
slipstream that could be seen especially during TNG and Voyager the ship always
appeared to be in some sort of tunnel through space which would have to be
similar with normal warp propulsion if it took place inside subspace.
Additionally
we know from TNG: "Where No One Has Gone Before", "Schisms"
and other occasions that subspace is a realm that is inhabitable but that ought
to look in some way different than normal space. Hence, it seems more likely that
the a ship using normal warp drive remains in our space. In this sense a
subspace field is not a field that opens a gate into subspace, but rather one
that allows subspace to "flow" into our space, making it more like
subspace or shielding it against our space like some sort of semi-permeable
wall.

Subspace field A
subspace field below 1 cochrane is a distortion of normal space for the most
part, so we may want to call it just a "space field" (but since
subspace includes space, the collective name "subspace field" is
definitely correct). The field is not strong enough to stretch down to the first
layer of subspace. But it has the effect of lowering the apparent mass of the
ship as observed from outside because of its special geometry. This effect of a
subspace field would be much the same if the ship were amidst the distortion,
but the stress would kill the crew and ultimately destroy the ship at above a
few hundred millicochranes. Instead of exposing the crew and spaceframe to such
a stress, all subspace fields, also and especially those above 1 cochrane, are
created in a way that a shell of high distortion envelops the ship which is safe
in a largely undistorted interior, as can be seen in Fig. 3.6.

The mass-lowering property of subspace fields is used in the impulse engines to facilitate
sublight propulsion through subspace driver coils in the impulse engines as stated in the TNGTM.
Once back in normal space, the exhausted plasma from the impulse engines gain
mass and because of the principle of momentum conservation the thrust increases accordingly -- the ship may have less powerful impulse engines and
needs to carry less fuel. For warp, on the other hand,
it may be just a beneficial side effect. The mass would have to be lowered
to zero to be able to reach light speed, which is impossible with any
field of limited energy content, even a warp field of above 1 cochrane.

Fig. 3.2 shows the power expenditure of a typical warp
drive. If we look at the first peak transitional threshold at Warp 1, we find
that the power rises strongly as the speed approaches the particular
threshold which is exactly at the speed of light, c. The power peak is almost
two decades high, but clearly not infinite. If, however, the mass can't be
lowered to zero, how can the threshold be passed with finite energy? The reason
must lie in some limited interaction of the subspace field below 1 cochrane with
the first subspace layer. While there may be no open gate that would allow
energy to flow into subspace or subspace to flow into normal space, some
tunneling may occur between the two, considering that the space distortion
lowers the threshold between the two domains. Any subspace or warp field does
the same in any other layer of subspace.

Symmetric warp field A symmetric warp field is a subspace field strong enough to shield a ship from normal space in a way that it takes on the frame of reference of subspace, while the ship itself is still in normal space. In order to become a warp field, the subspace stress has to be more than 1 cochrane. At 1 cochrane the field created by the subspace coils in normal space is strong enough to cross the threshold to the first subspace layer. Vice versa, subspace begins to flow into normal space. This subspace begins to "fill" the spatial distortion shell surrounding the ship, effectively shielding it against our universe.
If a symmetric warp field is created around a ship, it will remain in our universe, but it will be enabled to move as if it were in subspace. Only that a symmetric field itself does not move the vessel. It necessitates either an additional engine to achieve propulsion or, more elegantly, the warp field has to be tuned to become asymmetric and thereby propulsive.

We may surmise that many alien warp ships without distinct nacelles, especially those with rocket engines at the aft end, use symmetric warp fields and hence need the additional engines to push the ship forward. Federation starships, on the other hand, have additional engines just for sublight propulsion, while at warp only the warp nacelles are activated, creating a propulsive
asymmetric warp field.

Symmetric warp fields are in use in the computer cores of modern Federation starships as we know from the
TNGTM. With all of the devices and wires of the computer core embedded into a symmetric warp field, it is possible for the charge carriers inside to accelerate to FTL speeds. At the interfaces to external components the current slows down and is limited to light speed.

Asymmetric warp field
Asymmetric warp fields combine the mass-lowering and shielding properties of a
symmetric warp field with a propulsive effect. This may achieved through
creating a warp field by firing the coils in the nacelles such that the
extending fields created by the single coils keep pushing on each other and are
driven towards the aft end of the ship. This is about the explanation given in
the TNGTM. The book, however, does not distinguish between multilayered
fields that are needed for propulsion in the first place (because only through
interaction between the partial fields or rather waves created by the coils the
sum wave can have a preferred direction) on one hand and multilayered fields to
achieve higher warp speeds on the other hand. The difference will become obvious
in the following paragraph.

Multilayered warp field
In order to be propulsive at all, the single field components generated by the
warp coils must interfere or in some other fashion interact to create an
imbalance between the fore and the aft direction. Hence, such fields would have
to be of the same type, otherwise they could penetrate one another without such
an interaction. This is why we can assume that one single frequency of
energy is basically sufficient to drive the ship. Since frequency corresponds to
energy and energy corresponds to subspace levels, we may speculate that the
higher the frequency is, the deeper may the field extend into subspace. With
higher energy and/or higher frequency the starship may achieve higher warp
speeds.

It may be possible to achieve and maintain Warp 2, for
instance, with the warp field still tuned for Warp 1 if only enough power is
released into subspace to cross the Warp 2 threshold too. Looking at Fig. 3.2 again, we could extrapolate the curve piece
below Warp 1, for instance, to estimate which power would be necessary to achieve
Warp 2 with only one layer of the warp field. This would not really work out
quantitatively, because in that case the power usage would be many orders of
magnitude higher which is definitely a stretch because we wouldn't expect the
subspace layers to be that much different in whatever property matters for
propulsion. But qualitatively it may give us the reason why the frequency is
tuned first of all to reach a certain threshold and the warp factor assigned to
it. We can find an analogy in the real world in automobiles. Theoretically it
would be possible to accelerate up to 100km/h in the first gear. But no one
would do that because, aside from being highly inefficient, the engine and gear would not
survive that for long. It may be advantageous to create nested multilayered warp
fields instead of just one for the highest threshold because of the barrier
lowering, with each warp field paving the way for the next higher field.

Fig. 3.7 Examples of warp fields: Warp 1 (left), Warp 2 (right)

Warp factors Fig. 3.7 depicts subspace fields of two strengths whose
difference lies in how far they reach down into subspace. On the left image we
can see that the field causes a transition of subspace layer 1 which flows into
normal space. The right image depicts a stronger subspace field which
corresponds to layer 2. We can easily correlate the depictions to cochrane
values (TNG scale) and warp factors. On the left side we can see that the field
has just exceeded the first threshold from normal space with index 0 to the
subspace layer 1. It is a field of more than 1 cochrane and less than 10
cochranes, corresponding to speeds between Warp 1 and Warp 2. The field on the
right would have between 10 and 39 cochranes or Warp 2 to Warp 3. Fig. 3.7 does
not tell us anything about the structure of a warp field which, as was mentioned
above, usually consists of not a single but of nested layers. But we may imagine
that the sandwich structure of subspace is reflected by the structure of warp
field layers, the reason being that their cumulative interaction allows to exceed the higher thresholds (the ones deeper in subspace).

The Planck time In addition to the effect of coupled layers of subspace
fields the TNGTM mentions one more property of subspace fields that may
or may not be crucial for the working principle of the conventional warp drive.
While at warp, the ship appears to be at superluminal speeds
for less than the Planck time of 1.3*10-43s to the outside world. This suggestion
may originally come from Jesco von Puttkamer, NASA
director and scientific advisor of the first feature film, "Star Trek: The
Motion Picture". It seems that the mention in the TNGTM was included
rather as a homage to that first scientific attempt of explanation of warp
drive, because the Planck time is not needed once we postulate that actually the
different frame of reference of subspace allows FTL speeds. Well, unless
subspace were just a model for the effect conceived by von Puttkamer. The TNGTM creates the impression that
Cochrane's original drive
principle, the "continuum distortion propulsion" (CDP)
solely relied on the Planck time effect, rather than on subspace fields as they
are used in later designs. But there is nothing in canon Trek to support this
notion.

Energy conservation There is still one important property of warp drive still
to be discussed. Warp propulsion requires a constant power
output to maintain a certain speed or Warp factor. Once the power system fails,
the ship will drop out of warp and slow down to sublight speed (a speed which
will remain constant without acceleration because in motion in absence of a
subspace field is governed by Newton's laws).

One theory popular in fandom is that a so-called
"continuum drag" is the subspace equivalent to friction in classical
mechanics -- a force that constantly counteracts the acceleration force of the
ship and that increases with its speed. The continuum drag would be responsible
for slowing the ship down to sublight speeds once the warp engine fails. Once at
sublight speed, there would be no continuum drag any longer, and the friction
with interstellar particles would be usually almost negligible.

Subspace submersion and transwarp
Fig. 3.8 illustrates a different kind of warp field, one that allows a starship
to enter subspace entirely, without being surrounded by normal space. In Fig.
3.9 two of such funnels are combined inside subspace to a tunnel. It is obvious
that once in subspace a starship can move freely within this domain, without the
need to drag a subspace field along that extends from normal space into
subspace. It is possible that the power expenditure to maintain a certain speed
inside subspace is lower. Only crossing one or more thresholds to submerge into
subspace may consume considerably more energy than creating a normal warp field.

Fig. 3.8 Subspace submersion

Subspace submersion is employed in subspace
communications. The TNGTM mentions that signals are pushed into deep
subspace where they can propagate significantly faster. But without
amplification they will surface after some 20 light-years and thus slow down to
light speed. We can easily imagine that this effect is attributed to the
"continuum drag". Transwarp of the type used by the Borg seems to be
based on the same principle. The need to use pre-existing channels like first
mentioned in TNG: "Descent" and later shown in VOY:
"Endgame" corresponds with the high energy to push or drag the
whole ship into deeper subspace layers.

Fig. 3.9 Subspace channel

3.4 Subspace
Technology

Not yet available.

3.5
Subspace Phenomena

Not yet available.

See Also

Power & Propulsion
- about the right intermix ratio, warp inside a star system, how to stop a starship etc.